Air Flow in the Lungs: A simple model (with different parameters for different people) for the flow of air in and out of the lungs is V'(t)=-- -t , where V(t) (measured in liters) is the volume of air in 1)=-sin ( the lungs at time 20, t is measured in seconds, and t=0 corresponds to a time at which the lungs are full and exhalation begins. Only a fraction of the air in the lungs is exchanged with each breath. The amount that is exchanged is called the tidal volume. a) Find and graph the volume function V assuming V(0)=6 L. b) What is the breathing rate in breaths/minute? c) What is the tidal volume and what is the total capacity of the lungs?